One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. approximately how long is the side of the rhombus? (hint: diagonals of a rhombus bisect the angles.)

2 in.
3 in.
4 in.
5 in.

Approximately 3 inches.

Step-by-step explanation:

The shorter diagonal will bisect the 102 degree angle. so we have a triangle  with base angles of 51, vertex 180 - 102 = 78 degrees and base length 4 inches.

Applying the Sine Rule:

4 / sin 78 = x / sin 51  where x = the length of the  side of the rhombus.

x = 4 * sin 51 / sin 78

= 3.17 inches.

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720